A received baseband waveform for digital communication in white noise is
where s(t) is the transmitted pulse such that s(t) ∗ s(-t) is a Nyquist pulse, and g(t)is the channel impulse response. The received signal is passed through a filter matched to s(t) and sampled at lT. We are given the samples as our received data but we cannot observe the received signal at any point prior to the output of the sampler.
a. Derive the maximum-likelihood demodulator based on the observed samples, and describe an efficient implementation.
b. Would it be better to observe the received signal at the input to the matched filter?